In [1]}, [2]}, the authors K. Takasaki and T. Takebe defined the \(\hbar \) -dependent KP hierarchy (\(\hbar \) -KP hierarchy for short) by introduced a formal parameter \(\hbar \) . When \(\hbar \rightarrow 0\) , the \(\hbar \) -KP hierarchy becomes the dispersionless KP hierarchy, and when \(\hbar \rightarrow 1\) , it becomes the KP hierarchy. The tau functions and the wave function in \(\hbar \) -KP hierarchy are functions of parameters \(x,t_1,t_2,\cdots \) , while \(x\)  is only emerged in \(x+t_1\) . In this paper, we want the parameters are \(x=(x_1,x_2,\cdots )\) , which correspond to \((t_1,t_2,\cdots )\)  in [1]}, [2]}.
